function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta
J=mean(-y.*log(sigmoid(X*theta))-(1-y).*log(1-sigmoid(X*theta)))+(lambda./(2.*m)).*sum(theta(2:end).^2);

grad=mean(repmat((sigmoid(X*theta)-y),1,length(theta)).*X,1).'+(lambda./m).*[0;theta(2:end)];




% =============================================================

end
